COLLOCATION COMPUTATIONAL ALGORITHM FOR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

Abstract

. In this study, we present a collocation computational technique for solving Volterra-Fredholm Integro-Differential Equations (VFIDEs) via fourth kind Chebyshev polynomials as basis functions. The method assumed an approximate solution by means of the fourth kind Chebyshev polynomials, which were then substituted into the Volterra-Fredholm Integro-Differential Equations (VFIDEs) under consideration. Thereafter, the resulting equation is collocated at equally spaced points, which results in a system of linear algebraic equations with the unknown Chebyshev coefficients. The system of equations is then solved using the matrix inversion approach to obtain the unknown constants. The unknown constants are then substituted into the assumed approximate solution to obtain the required approximate solution. To test for the accuracy and efficiency of the scheme, six numerical examples were solved, and the results obtained show the method performs excellently compared to the results in the literature. Also, tables are used to outline the methods accuracy and efficiency.